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Math Help - communication function problems

  1. #1
    Senior Member euclid2's Avatar
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    communication function problems

    1. Find an example of a function that produces the same image when its graph is reflected in the y axis as it does when its graph is reflected in the x axis.

    2. find a function that is equal to its own inverse

    3. how many different functions are there that are equal to their own inverse?

    Please help-
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    1. Find an example of a function that produces the same image when its graph is reflected in the y axis as it does when its graph is reflected in the x axis.
    how about any circle centered at the origin?

    2. find a function that is equal to its own inverse
    how about the line y = x?

    3. how many different functions are there that are equal to their own inverse?
    infinitely many

    how about trying it? tell me a family of functions that will satisfy this. think in terms of graphs. do you know what finding the inverse means graphically?
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Jhevon View Post
    how about any circle centered at the origin?

    how about the line y = x?

    infinitely many

    how about trying it? tell me a family of functions that will satisfy this. think in terms of graphs. do you know what finding the inverse means graphically?
    Can you give me an example of an equation for 1.?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    Can you give me an example of an equation for 1.?
    i can, but i won't

    as i said, ANY circle centered at the origin will do. just come up with one. you know what the equation of a circle centered at the origin looks like, right? if not, you should. look it up
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  5. #5
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Jhevon View Post
    i can, but i won't

    as i said, ANY circle centered at the origin will do. just come up with one. you know what the equation of a circle centered at the origin looks like, right? if not, you should. look it up
    (x - h)2 + (y - k)2 = r2
    Is this the equation you are speaking of?
    although why are you mentioning circles if a circle is not a function
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    (x - h)2 + (y - k)2 = r2
    Is this the equation you are speaking of?
    although why are you mentioning circles if a circle is not a function
    ah, yes, function, haha . i was thinking of graphs

    ok, think "odd function" here. what examples can you come up with? do they work?
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    Senior Member euclid2's Avatar
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    Quote Originally Posted by Jhevon View Post
    ah, yes, function, haha . i was thinking of graphs

    ok, think "odd function" here. what examples can you come up with? do they work?
    Perhaps f(x)= 1/x?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    Perhaps f(x)= 1/x?
    yes, that works.

    i would have expected you to try something simpler, but that's fine
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